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作者机构:Mathematics and Computer Science Division Argonne National Laboratory Argonne IL 60439 USA Department of Industrial and Systems Engineering University of Wisconsin-Madison Madison WI 53706 USA IMB Université Bordeaux 1 RealOpt INRIA Bordeaux Sud-Ouest 33405 Talence France
出 版 物:《Journal of Physics: Conference Series》
年 卷 期:2009年第180卷第1期
摘 要:The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.